A correspondence-less approach to matching of deformable shapes

Authors:
Jonathan Pokrass;Alexander M. Bronstein;Michael M. Bronstein
Affiliations:
Dept. of Electrical Engineering, Tel Aviv University, Israel;Dept. of Electrical Engineering, Tel Aviv University, Israel;Inst. of Computational Science, Faculty of Informatics, Università della Svizzera Italiana, Lugano, Switzerland
Venue:
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Year:
2011

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Abstract

Finding a match between partially available deformable shapes is a challenging problem with numerous applications. The problem is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise correspondence between the two. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use diffusion geometric descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular meshes. Experiments demonstrating the success of the proposed method are presented.